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Find the general solution of trigonometric equations with n·π or n·2π notation for all infinite solutions.
Key: n represents any integer. Adding n·(period) gives all solutions.
Trig functions are periodic - they repeat forever. If θ = 30° is a solution to sin(θ) = 0.5, so is θ = 30° + 360°, 30° + 720°, 30° - 360°, etc. The n captures all these infinite solutions in one formula.
Tangent has period π (180°), not 2π. It repeats twice as often as sine and cosine, so solutions are spaced 180° apart instead of 360°.
For sin(θ) = k, the two solutions in [0°, 360°) are arcsin(k) and 180° - arcsin(k). For cos(θ) = k, they are arccos(k) and -arccos(k), which simplifies to ±arccos(k).